On the Effect of Measurement Error with Linearly Increasing-Type Variance on Simultaneous Monitoring of Process Mean and Variability

Abstract

In most quality control applications, the errors generated from measurement system can adversely affect the ability of control charts in detecting out‐of‐control conditions. In this paper, the effect of measurement error with linearly increasing‐type variance on the performance of maximum exponentially weighted moving average and mean‐squared deviation (MAX‐EWMAMS) control chart is studied. For this purpose, different out‐of‐control scenarios including mean shifts, variance shifts, and simultaneous shifts in both are considered, and the detecting performance of the proposed approach is investigated through simulation study. The results of simulation study in terms of three criteria including average run length, standard deviation of run lengths, and the empirical distribution of run lengths prove that the measurement error with linearly increasing‐type variance can adversely affect the performance of MAX‐EWMAMS control. Copyright © 2015 John Wiley & Sons, Ltd.

The effect of measurement errors on the adaptive EWMA chart

“…In some environments, the measurement error variance changes linearly with the process level. The effect of measurement errors with both constant and linearly increasing variance is discussed in some papers [19][20][21] and Hu et al 24 The effect of measurement errors on multivariate quality characteristics is also evaluated by other studies [25][26][27][28] and Maleki et al 29 For more literatures on the simultaneous monitoring of process mean and variability, refer to previous studies [29][30][31][32][33] and references cited therein.…”

The performance of the adaptive EWMA median chart in the presence of measurement error

“…But, in practice, an exact measurement is a rare phenomenon in any of the situations where human involvement is evident. The effect of measurement errors has been intensively investigated for a number of mean‐ or variance‐type charts, and the conclusion is that the performance of these charts is always negatively affected in presence of such errors, see, for instance, Linna and Woodall,() Maravelakis et al, Shore, Chang and Nikzad, Chakraborty and Khurshid, Amiri and Nikzad, Khati Dizabadi et al, Ghashghaei et al, Tran et al, Daryabari et al, Sabahno and Amiri, Castagliola et al, and Salmasnia et al …”

“…But, in practice, an exact measurement is a rare phenomenon in any of the situations where human involvement is evident. The effect of measurement errors has been intensively investigated for a number of mean-or variance-type charts, and the conclusion is that the performance of these charts is always negatively affected in presence of such errors, see, for instance, Linna and Woodall, 25,26 Maravelakis et al, 27 Shore, 28 Chang and Nikzad, 29 Chakraborty and Khurshid, 30 Amiri and Nikzad, 31 Khati Dizabadi et al, 32 Ghashghaei et al, 33 Tran et al, 34 Daryabari et al, 35 Sabahno and Amiri, 36 Castagliola et al, 37 and Salmasnia et al 38 The measurement errors model the most commonly used in the literature is the linear covariate model, proposed by Linna and Woodall,25 ie, Y = A + BX + , where A and B are known constants and is a random error due to the measurement imprecision. In this paper, they investigated the properties of the ShewhartX and the S 2 charts with measurement errors, and they suggested taking multiple measurements to compensate for the effect of measurement errors, Maravelakis et al 27,39 evaluated the performance of the EWMAX and the CUSUMX charts, respectively, in the presence of measurement errors using the same linear covariate model.…”

Joint Monitoring of Process Location and Dispersion Based on CUSUM Procedure and Generalized Likelihood Ratio in the Presence of Measurement Errors

“…They also provided a cost function analysis to determine the optimal number of multiple measurements and the sample size to reduce the effect of TCME. Khati Dizabadi et al investigated the effect of measurement errors with linearly increasing‐type variance on the performance of maximum exponentially weighted moving average and mean‐squared deviation control chart to detect out‐of‐control scenarios. The effect of contaminated data due to the gauge measurement errors on the performance of ELR control chart under ranked set sampling procedure is explored by Ghashghaei et al .…”